On a parabolic partial differential equation and system modeling a production planning problem

Abstract

<abstract><p>We consider a parabolic partial differential equation and system derived from a production planning problem dependent on time. Our goal is to find a closed-form solution for the problem considered in our model. Our new theoretical results can be applied in the real world.</p></abstract>

Exact Solution for the Production Planning Problem with Several Regimes Switching over an Infinite Horizon Time

“…When w i is correlated with correlation ρ, the HJB system (10) becomes which has the same solution as (10), due to the mixed derivative terms (see [17] for details).…”